Question

Suppose the figure below represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass (Δx in mm), given that the incident angle is 37.5° and the glass is 2.75 cm thick.

______ mm

Answer 1

Assumption : Refractive index of air (n₁)= 1 ; Refractive index of crown glass (n₂)= 1.52 and Refractive index of water (n₃)= 1.33

Diagram :

Solution :

In the figure , the doted line represents hypothetical ray in absence of crown glass.

Using snell's law to find angle ₂

n₁sin₁ = n₂sin₂

= 23.61°

There are two triangles, smaller triangle represents actual ray after crown glass while larger triangle represents hypothetucal ray without crown glass. The height of triangles is 2.75 cm.

Now For smaller triangle

By sine law  

= 1.20 cm

For larger triangle

By sine law

= 2.11 cm

Now amount of ray displaced by crown glass is given by:

x = l₂ -l₁

= 2.11 cm - 1.20 cm

= 0.91 cm ( 9.1mm)

Answer : 9.1 mm